1) the deportations could have resulted in a bar.
2) he cannot adjust status in the US. To immigrate, if at all possible, he will need waivers and will need to process abroad.
You need to retain an experienced immigration lawyer to review all the facts, advise you, and handle the case. You can find one through http://www.ailalawyer.com.
J Charles Ferrari Eng & Nishimura 213.622.2255 The statement above is general in nature and does not constitute legal advice, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship. Answers on Avvo can only be general ones, as specific answers would require knowledge of all the facts. As such, they may or may not apply to the question.
Having re-entered the US after he was deported is a very bad thing for him.
Meet with an attorney.
Unfortunately, even marriage to a US citizen doesn't 'save' everyone.
PROFESSOR OF IMMIGRATION LAW for over 10 years -- This blog posting is offered for informational purposes only. It does not constitute an attorney-client relationship. Also, keep in mind that this is an INTERNET BLOG. You should not rely on anything you read here to make decisions which impact on your life. Meet with an attorney, via Skype, or in person, to obtain competent personal and professional guidance.
This is a very complex case. He will not be able to adjust his status without leaving the US and without multiple waivers. This is not a case you should attempt to handle on your own, because the approval rates are very, very low. Meet with an attorney to discuss your options.